Distribution of Cross-Section of Price Changes and Measurement of Inflation

In this study we look at the statistical properties of components forming the Wholesale Price Index (WPI), the headline inflation index for the Indian economy. We find that not only is the distribution of price changes at the disaggregate level highly leptokurtic, but also the cross-sectional distribution of price changes is positively skewed. This has the implication that the weighted mean would fail to be an efficient estimator of inflation. Trimmed Means, belonging to the class of limited influence estimators, have been used by many central banks to get around the skewness problem. We also explore the use of trimmed means for efficiently estimating inflation for India. In particular, we study the robustness of trimmed means to the benchmark (Centered Moving Average vs. trends derived from the Hodrick Prescott Filter) and the evaluation criteria (Mean Absolute Deviation vs. Root Mean Square Error vs. an Asymmetric Loss Function). Although we study the performance of trimmed means against the weighted mean in some detail, we stop short of proposing any ‘one’ trimming pattern as the ideal. The selection of the headline inflation rate depends as much on its ability to track the underlying trend void of transitory disturbances as much on its ability to forecast future inflation and its correlation with money growth, something we don’t deal with in the present study.